Linear & Angular Kinematics II

Linear and Angular Kinematics II

Key Concepts to Understand

  • Relationship between the axis of rotation and the plane of motion.

  • Basic metrics for describing angular kinematics:

    • Direction and sign of motion.

    • Angular velocity and angular acceleration.

  • Importance of directional coordinate systems for class discussions.

Axes of Rotation

  • Movement Dynamics:

    • Joints turn around an axis that has a 90-degree relationship to the plane of motion.

  • Named Axes of Rotation:

    • Mediolateral Axis of Rotation

    • Anteroposterior Axis of Rotation

    • Longitudinal Axis of Rotation

Rotary (Angular) Motion

  • Definition:

    • Movement of a segment involves each point moving through the same angle simultaneously while maintaining a constant distance from the center of rotation.

Degrees of Freedom

  • Movement Options for a Segment:

    • A completely unconstrained segment has 6 degrees of freedom.

    • More constrained segments retain fewer degrees of freedom

    • Unconstrained segment can rotate around each of the 3 axes

      • 3 planes x 2 direcions = 6 options for movement

Comparison: Linear vs. Rotary Motion

  • Linear Motion:

    • Measured in meters (m).

  • Rotary Motion:

    • Measured in radians (rad).

    • Conversion Note:

    • 1 radian ~ -57.3 degrees

    • 2 radians = 360 degrees

Converting Degrees to Radians

  • Conversion Formula:

  • Degrees from Radians:

Direction of Rotation

  • Clockwise: Denoted as negative (-).

  • Counterclockwise: Denoted as positive (+)

  • Clockwise (-) vs. Counterclockwise (+)

Vector Magnitudes in Rotational Movement

  • Angular Velocity (ω):

    • Measured in radians per unit time.

  • Linear Velocity (V):

    • Position versus time relations.

Angular Kinematic Example

  • Example Data for Angular Displacement Calculation:

    • Required Measurements:

      • Starting Position

      • Ending Position

    • Calculation of Angular Displacement:

    • Starting position: π\pi /-6 rad

    • Ending position: π\pi /6 rad

    • Angular Displacement = π\pi /3 rad

    • Change in Time = 3 seconds

    • Angular Velocity = π\pi /rad/s

    • Answer: 0.35 rad/s

Angular Acceleration

  • Definition: Rate of change of angular velocity with respect to time

  • Formula for angular acceleration (α):

  • α\alpha = Δ\Delta ω\omega (rad/s) / Δ\Delta t (s)

Example of Angular Acceleration Calculation

  • Data Points:

    • Starting Velocity: 0 rad/s

    • End Velocity: -π/2 rad/s

    • Change in Time: 4 seconds

    • Calculation:

Defining Our Coordinate System (Part 2)

  • X-axis (Mediolateral Axis): Positive is to the right, negative is to the left.

  • Y-axis (Anteroposterior Axis): Positive is anterior, negative is posterior.

  • Z-axis (Longitudinal Axis): Positive is superior, negative is inferior.

Upcoming Lectures and Topics

  • 1/13: Introduction to Biomechanics and Motor Control, Reading FB: Chapter 1

  • 1/15: Linear and Angular Kinematics (position, displacement, velocity), Reading FB Chapter 2

  • 1/20: Linear and Angular Kinematics II, Reading FB Chapter 3
    (Acceleration and application, right hand rule)

  • 1/22: Forces in Human Movement, Reading Chapter 5

  • 1/27: Ground Reaction Forces, Reading Chapter 6

  • 1/29: Ground Reaction Forces In-Class Lab, Guide on Canvas

  • 2/3: Muscle Mechanics I, Focus on Torque

  • 2/5: Muscle Mechanics II, Focus on (force-length, force-velocity)

  • 2/10: Exam #1